Answer:
If you feel the climax occurs when the play that Hamlet devises proves Claudius’ guilt, then you should include the following points:
Hamlet contemplates killing his uncle.
Hamlet does not go through with the murder, as he is unsure of his uncle’s guilt.
Hamlet tests his uncle’s guilt through a reenactment of the murder of King Hamlet.
Claudius reacts to the scene in which the King’s murder is performed.
Hamlet finally realizes that his uncle is guilty, and from this point on, Hamlet puts to rest any doubts he had about his uncle’s innocence.
As Hamlet’s doubts are put to rest at this moment, this point in the play can be considered the climax.
If you feel the climax occurs when Hamlet stabs Polonius, then you should include the following points:
Hamlet contemplates killing his uncle.
Hamlet does not go through with the murder as he is unsure of his uncle’s guilt.
Hamlet spends much time contemplating whether to kill his uncle and procrastinates over the deed.
He doesn’t act and only tests his uncle’s innocence through the performance of a play in which a king is murdered in a manner similar to King Hamlet’s murder.
Even after Claudius appears guilty, Hamlet refuses to kill his praying uncle and postpones the deed even further.
In Queen Gertrude’s room, Hamlet believes Claudius is hiding behind the tapestry and impulsively stabs his sword in that direction, killing Polonius.
Because Hamlet finally acts upon his desire to kill Claudius, this point in the play can be considered the climax.